‘Resi^t/ances^  rheo^tai;**  a>x<i 
clec't.v'ic-  appavat/us, 


RESISTANCES,  RHEOSTATS  AND  ELEC- 
TRIC HEATING  APPARATUS.* 


Harold  B.  Smith,  M.  E. 


The  operation  of  nearly  all  apparatus  for  the  production 
or  utilization  of  electric  currents  involves,  at  some  one  or 
more  points  in  the  system,  the  use  of  rheostats  or  other  de- 
vices by  which  variable  resistances  may  be  inserted  in  one 
or  more  circuits  and  controlled  either  automatically  or  by 
hand  regulation. 

The  materials  most  commonly  used  for  resistance  are 
German  silver  and  iron  wire  which  is  usually  galvanized. 
The  materials  less  commonly  employed  are  aluminum, 
copper,  carbon,  graphite,  water  and  alloys  of  platinum  and 
manganese.  The  alloys  of  platinum  and  manganese  are 
used  principally  in  instrument  work  on  account  of  their 
low  temperature  coefficients  and  high  specific  resistance. 
Resistance  rods  of  practically  any  desired  resistance  may 
be  made  of  a mixture  of  clay  and  graphite  in  proportions 
which  depend  upon  the  resistance  desired. 

Primarily  then,  the  design  of  a resistance  or  rheostat 
depends  upon  calculations  based  upon  the  dimensions  and 
physical  properties  of  the  materials  selected  and  the  two 
important  points  to  be  predetermined  are  the  temperature 
when  in  operation  and  the  actual  resistance  at  that  temper- 
♦Copyright,  1898,  by  Harold  B.  Smith.  All  rights  reserved. 


■'’n 

y 


2 


ature.  These  may  be  approximated  with  a sufficient 
degree  of  accuracy  for  many  cases  by  simple  approxima- 
tions rather  than  to  make  use  of  the  more  exact  methods 
given  later  which  involve  a greater  amount  of  calculation* 

R = ^ , (i) 

me 

where ; 

R = the  resistance  in  international  ohms. 

L = the  length  in  feet  of  the  resistance  conductor. 

me  = the  number  of  circular  mils  in  the  cross  section  of 
the  resistance  conductor. 

Kt  = the  resistance  in  international  ohms  per  circular 
mil  foot,  of  the  material  employed,  at  the  tempera- 
ture t. 


TABLE  I. 


Approximate  Values  of  K* 


Degrees 

Temperature 

1 

Copper 

(Annealed) 

Alum  num 
(Annealed) 

Iron  1 

(Annealed)  1 

GERMAN  1 

SILVER 

Cu.— 4 pts. 
Ni.— ■ ” 

Zn. — I “ 

PLATINUM 

SILVER 

Pt.  — a pts. 
Silv.  — I *•  1 

gin 

SuSf?; 

Cent. 

Fahr. 

o 

32 

9.6 

17*5 

58.4 

125-9 

146.7 

253-7 

lO 

50 

10. 0 

17.9 

58-8 

126.3 

147.0 

.-J20 

68 

10.4 

18.3 

S9-3 

126.8 

147-3 

ri 

30 

86 

10.8 

18.7 

59-8 

127.2 

147.6 

t-t 

a 

-4-> 

40 

104 

II. 2 

19.1 

60.2 

127.7 

147.9 

CO 

C 

50 

122 

II. 6 

19.4 

60.7 

128.1 

148.3 

0 

0 

60 

140 

12.0 

19.8 

61. 1 

128.5 

148.6 

70 

158 

12.4 

20.2 

61.6 

129.0 

148.9 

80 

176 

12.8 

20.8 

62.0 

129.4 

149.2 

.0 

*-Cj 

100 

212 

13*5 

21.4 

62.9 

130*3 

149.8 

0 

oJ 

150 

302 

15*4 

23*4 

65.2 

132.5 

151-3 

u 

200 

392 

17.4 

25*3 

67.4 

134*7 

152.9 

3 


The  following  table*  is  frequently  of  greater  service 
than  the  last. 


TABLE  II. 


Resistance  of  Conductors  at  20°  C. 


Material 

K, 

Temperature 

Coefficient 

Authority 

for 

Temp.  Coef. 

Silver,  Annealed 

9-65 

.00377 

Riviere 

Copper,  Annealed 

10.3 

.00388 

Matthiessen 

Copper,  Hard  Drawn 

10.5 

.00388 

i i 

Aluminum,  Annealed 

18.73 

.00390 

Benoit 

Zinc,  Compressed 

36.0 

.00365 

Matthiessen 

Platinum,  Annealed 

56.69 

.00247 

Benoit 

Iron 

63.21 

-00453 

a 

Tin 

84-57 

-00365 

Matthiessen 

German  Silver 

126.0 

.00044 

Mascart 

Lead 

126.1 

.00387 

Matthiessen 

Platinoid 

205.4 

.00021 

it 

Manganin  A 

258.7 

negligable 

Helmholtz 

Manganese  Steel 

419.0 

.00122 

Fleming 

Mercury 

577-6 

.00889 

Mascart 

Manganin  B 

643.6 

negligable 

Helmholtz 

Bismuth,  Pressed 

845.2 

•00354 

Matthiessen 

Graphite 

6734- 

— .0009 

Joubert 

Arc  Light  Carbon 

37920. 

— .00052 

( ( 

Slight  discrepancies  in  the  two  tables  occur  because  of 
differences  in  tests  of  slightly  varying  samples. 

If  the  resistance  is  designed  to  create  a definite  fall  of 
potential  in  the  circuit,  the  value  of  which  is  E,  then  the 
cross  section  necessary  to  secure  that  fall  of  potential  with 
a given  length,  L,  in  feet,  carrying  the  current,  i,  is, — 


*A.  B.  Herrick,  Electrical^Engineer  Data  Sheets,  5711-5. 


4 


m. 


Kt  X L X i 
E 


(2) 


The  temperature  of  the  resistance  conductor  when  ex- 
posed to  still  air  may  be  approximated  from  the  expression 

T= - (3) 

1 X .053  + A X K, 

where : — 

T = temperature  above  the  surrounding  air  in  degrees 
centigrade. 

P = watts  radiated  from  the  surface. 

A = surface  in  sq.  in.  available  for  radiation. 

1 = length  of  conductor,  or  coil,  in  feet. 

K,  = constant  which  may  be  taken  as  .004  for  bright 
metallic  surfaces  and,  depending  upon  conditions, 
as  high  as  .012  for  rough  black  surfaces. 

Where  greater  facility  of  calculation  than  can  be  secured 
by  the  above  method  is  essential,  the  following  modification 
of  a method  proposed  by  Mr.  G.  Rennerfeltf  may  be 
employed. 

For  any  form  of  cross  section  of  conductor  used  for  a 
resistance  we  have  : — 

P = m\/x  (4) 

where, — 

P = the  perimeter  of  the  cross  section. 

X = the  area  “ “ “ 

m = a constant  depending  upon  the  form  of  cross  section. 
For  a square,  m = 4 and  for  a circle  m = 2 which 


♦ A.  E.  Kennelly,  Heating  of  Conductors  by  Electric  Currents,  Elec- 
trical World,  Vol.  14.,  p.  336. 

A.  V.  Abbott,  The  Electrical  Transmission  of  Energy,  pp.  289-293. 

C.  E.  Timmerman,  Trans.  Am.  Inst.  Elect.  Eng’s.,  Vol,  10,  p.  342. 
t G.  Rennerfelt, ' Formulae  for  Resistance  Coils,  Elect.  World,  Vol. 
23,  p-  241. 


5 


is  the  smallest  value  possible  for  m and,  for  this  reason  and 
convenience  in  manufacture,  circular  sectioned  conductor 
is  always  used,  except  it  be  for  some  special  reason,  such 
as  the  frequent  necessity  of  securing  a grea*ter  proportion 
of  radiating  surface  to  area  of  cross  section,  when  rectang- 
ular or  corrugated  conductor  is  used. 

For  any  form  of  cross  section  where  m is  known  we 
have, — 

S = py  (5) 

= ymv'x  (6) 

= fi^R  (7) 

where, 

S = surface  of  conductor  in  sq.  in. 

^y  = length  of  conductor  in  inches. 

f = number  of  sq.  in.  for  each  watt  radiated. 

Then, — 

ym\/x  = f FR  (8) 

and  from  equation  (i)  we  may  write, 

R = (9) 

where  Kj  is  the  specific  resistance  of  the  material  employed. 
This  may  be  calculated  from  the  Matthiessen  formula  for 
resistance, 

K,  =-K3(i  +at±bt2)  (lo) 

where  t is  the  temperature  in  degrees  centigrade  and  Kg  is 
the  resistance  at  zero  centigrade. 


6 


TABLE  II. 


Material 

K3 

a 

b 

Copper  . 

.00000066 

.0038 

.00000126 

Aluminum 

.0000013 

.0038 

.00000126 

Iron 

.0000040 

.0048 

.00000126 

German  Silver 

.0000090 

.00044 

.000000152 

Combining  (8)  and  (9)  we  have, — 
ymy^x  = fi^R 

= fi2y.K, 


Whence,  mx\/x  = f i K. 

mx 


=v 

=v 


m2 

(ii) 

m2 

(12) 

which  give  expressions  for  the  area  of  cross  section  of 
conductor. 

To  determine  the  length  of  conductor  we  can  place  in 
K V 

equation  (8)  x=— which  comes  from  (9)  and  gives, — 
R 


ym 


' R 


fi^R 


(13) 


7 


y2  y 


f2  i4  R3 


= 

K,  m2 


iRri  (14) 


as  the  length  of  conductor  in  terms  of  current,  radiation, 
cross  section  and  resistance. 

In  a similar  manner,  we  may  express  the  weight  of 
the  conductor  as, — 


W = s.x.y 


which  we  get  by  substituting  the  values  of  x and  y from 
equations  (12)  and  (14)  and  where, — 

W = total  weight  of  conductor  in  pounds, 
s =::=  weight  per  cubic  inch  of  material  employed. 

The  above  forms  the  basis  of  the  method  of  calcula- 
tion, but  as  the  resulting  equations  would  be  cumbersome 
for  ordinary  use,  the  following  table  gives  numerical  values 
for  most  of  the  terms  which  may  be  substituted  in  the 
formulae. 


TABLE  III. 


O fOOO  VO 
cs  Om>*  O 
CO  O 


a 

cu 

h 


Ph 

a 

tu 

h 


VO  COVO  c^ 
O VO  VO  VO 
M M CO 
O O O O 
O O O O 
O O O O 


Iw 


i:^  rh  0\  M 

i:^  CO  c^  O 

i^^OO  ci  i:^ 
G\  !>>  VO  ^ 


M 00  M CO 
O 0\  M 

M M M 

o o o o 


IM 


CO 

VO  On  OvVO 
On 

O H CO  rj“ 

O O O O 

o o o o 
o o o o 


NO  c^  J>. 
VO  O t-i  CO 


cs  M VO 
O 00  VO  Tt- 


VO 

!>.  C^  M H 
ON  (N  00  M 
O M H M 

O O O O 


VO 

i:^  J>-  On  O 
00  CO  ON  Tf 

O M M 

O O O O 
O O O O 
O O O O 


Im 


O CONO 

CO  vooq  NO 

NO  VO 
O 00  VO 
M 


VO 

CO  CO  O 
On  M !>.  H 
O M M C^ 
O O O O 


03 
I.— I 


a 

p 

u P 

p.’g 

uc 


(/} 


c u 
o <v 


I 

CM 

CO 

; o 

o 

Th 

On 

VO 

00 

cq 

M 

M 

CO 

O 

O 

o 

00 

CM 

q 

VO 

vq 

VO 

CM 

M 

CM 

CM 

'no 

VO 

O 

O 

NO 

vq 

vq 

ON 

H 

M 

M 

o 

O 

j>- 

M 

M 

VO 

vq 

cq 

M 

M 

H 

M 

00 

CO 

VO 

M 

VO 

CO 

J>. 

CM 

M 

M, 

M 

o 

o 

O 

o 

q 

o 

o 

o 

M 

M 

H 

M 

VO 

M 

VO 

CO 

CM 

00 

cq 

00 

vq 

M 

CO 

CM 

o 

NO 

CO 

vq 

vq 

lO 

M 

o 

o 

CO 

On 

vq 

q 

Nq 

CO 

CM 

1 

1 

a 

1 

1 

1 

1 

1 

-t-j 

-t-> 

o3 

6r* 

m 

u 

<v 

(X 

1 

1 

u 

dJ 

w 

1 

1 

a 

cr 

If) 

II 

M Imh 

1 0^ 

(N 

€r 

M 

M 

M 00 

• • 

VO  NO 

CM 

CM  o 

M 

M 

p- 

M 

• • 

NO 

M 

CM  O 

M 

CO 

M 

rh  VO 

• • 

l:^ 

o 

CM  O 

M 

H 

CM  ON 

, , 

00 

On 

CM  o 

00 

H 

M Th 

, , 

On  00 

00 

CM  O 

00 

H 

M o 

. . 

O On 

cq  q 

M 

1 CO  00 

•-I  On 

VO 

cq>  q 

M 

NO . VO 

• • 

CM  O 

VO 

CO  M 

M 

CM  !>. 

• • 

M 

CO  H 

M 

H O 

• • 

NO 

CO 

cq  M 

M 

CM  VO 

• • 

00  ^ 

CM 

CO  M 

(U 

u 

00 

a 

On  VO 

P 

CO  M 

cr 

if) 

IV 

O 'O 

Ij 

CO  00 

u 

xt"  c-i 

0 

S-l 

^ ^ 

o p 

i<N  1®L 

a;.S 

” 1 fi  fi 

^ tj 
a dj 

if) 

if) 

V ^ 

9 


In  case  it  is  desirable  to  arrange  the  circuit  so  as  to 
place  two  or  more  conductors  in  parallel  with  each  other, 
the  calculation  is  modified  so  that,  if  there  are  n conduc- 
tors in  parallel  with  each  other,  the  value  of  m is  y^n  times 
as  great  as  the  value  of  m for  a single  one  of  the  conduc- 
tors. Hence  in  table  V.,  we  must  multiply  the  values 


of  -I-  by  — and  the  values 
m^  n 


If  two  conductors  are  used  in  place  of  one  and  under 
the  same  conditions  otherwise  with  respect  to  radiation 
from  surface,  then  the  total  cross  sections  will  be  reduced 
to  = 79%  and  the  weight  to  =6^(fo-  With  three 
conductors  in  place  of  one,  the  cross  section  is  reduced  to 
6o%  and  the  weight  to  48%.  While  this  may  result  in 
decreased  cost  of  material  the  increased  cost  of  con- 
struction may  more  than  compensate  and  the  two  points 
should  be  considered  with  reference  to  each  other. 

Low  resistances  of  considerable  current  capacity  usually 
require  iron,  carbon,  water  or  alloys  composed  largely  of 
iron  as  the  resistance  material  because  of  the  prohibitive 
cost  of  other  materials  for  the  weights  required.  Carbon, 
graphite  and  iron  alloys  have  a resistance  so  variable 
with  slight  variation  in  composition  that  calculations  for 
their  use  can  be  made  only  when  based  upon  experimental 
data  from  samples  of  the  material  to  be  used. 

For  water  resistances,  the  following  table*  may  be  used 
as  a basis  for  calculations. 


‘E.  A.  Merrill,  Tables  and  Formulas,  p.  89. 


lO 


TABLE  VI. 

Approximate  Resistance 

Water  (hydrant) 

> 

100  ohms 

“ with  .25  per  cent,  salt  by  weight. 

7.84  “ 

“ “ -46 

(i  ((  (( 

4-65  “ 

“ “ .70 

( ( n a 

3.12  “ 

“ “ -93 

it  n n 

K) 

Cj 

00 

“ “ I. 16 

( ( ( ( ( ( 

1.90  “ 

“ “ 1-39 

((  a a 

1.48  “ 

“ “ .174 

‘ ‘ commercial  sulphuric  acid  4.12  “ 

“ “ -437 

((  (( 

“ 1.75  “ 

“ “ .724 

( ( ( ( ( ( 

“ I.IO  “ 

“ -985 

( ( ( ( ( ( 

bo 

Ln 

The  resistances 

given  in  the  table  are 

for  a cubic  foot  ot 

solution  between  plate  terminals. 

Where  salt  or  acid  is  used  in  the  water,  thin  plates  of 
carbon  are  desirable  terminals  as  iron  is  subject  to  rapid 
corrosion.  If  iron  plate  terminals  are  used,  sulphate  of 
soda  may  be  employed  to  reduce  the  resistance  of  the 
water. 

Tanks  for  water  resistances  should  be  so  proportioned 
as  to  allow  about  eight  watts  radiation  per  square  inch 
of  external  surface,  though  this  necessarily  depends  on 
conditions  of  operation.  For  example,  an  ordinary  barrel 
having  a surface  in  the  neighborhood  of  2500  sq.  in.  is 
capable  of  absorbing  20  Kw.  from  an  electric  circuit. 
About  one  ampere  per  square  inch  of  surface  of  electrode 
exposed  toward  opposite  electrode  may  be  allowed. 

For  resistances  of  covered  wire  wound  on  spools  or 
bobbins  a modification  of  Esson’s  expression*  may  be  used 
to  calculate  the  rise  in  temperature, 

’•'S.  P.  Thompson,  Dynamo-Electric  Machinery,  Vol.  i,  p.  374.  A.  H. 
and  C.  E.  Timmerman,  Trans.  Am.  Inst.  Elect.  Eng’s,  Vol.  10,  p.  336. 


II 


K^XP 

A 


(i6) 


where  may  be  given  a value  from  50  to  120,  de- 
pending upon  surrounding  conditions.  For  still  air  and 
varnished  surfaces,  this  value  may  be  taken  at  from  55  to 
70,  and  for  coils  encased  in  rough  blackened  metallic  sur- 
faces, it  may  be  from  80  to  95.  A is  the  entire  surface  in 
sq.  in.  available  for  radiation. 

Before  the  final  calculation  of  resistance  and  tempera- 
ture can  be  made,  it  is  necessary  to  decide  definitely  upon 
the  exact  method  of  mounting  and  arranging  the  resist- 
ance material,  which  cannot  always  be  done  before  ap- 
proximate calculations  are  carried  through,  but  should  be 
done  as  soon  as  possible,  as  the  radiation  coefficients 
depend  largely  upon  this  decision. 

In  rheostats  where  it  is  necessary  to  subdivide  the  resist- 
ance, modern  practice  indicates  the  following  : — 
for  dynamo  field  rheostats  of  all  voltages, 

n ==  7 if^Kw -f- 20  (17) 

for  motor  starting  and  speed  regulating  resistances, — 
n = 2i^Kw  + .5  y/v  (18) 

for  theatre  dimmers,  — (120  volts) 

n = 20]^Kw  (19) 

where  v is  the  voltage  of  the  circuit  and  n is  the  average  of 
several  representative  manufacturers  for  the  number  of 
subdivisions  or  steps  in  the  resistance.  The  number  of 
contacts  would  then  be  n + i or  n + 2 in  case  an  extra 
" dead  ” contact  be  used. 

The  least  area  of  surface  which  should  be  exposed  by 
each  contact  to  the  contact  arm  may  be  determined  from 
the  following  table  but,  in  many  cases,  there  should  be 


12 


provided  a greater  area  than  is  there  indicated  in  order  to 
present  sufficient  surface  and  material  for  mechanical  dur- 
ability and  strength  of  construction.  Phosphor-bronze 
forms  desirable  contacts  and  renewable  carbon  brushes  on 
the  contact  arm  may  be  employed  to  advantage  where  the 
conditions  of  operation  are  particularly  severe. 

TABLE  VII. 

Kind  of  contact.  Amperes  per  Sq.  In. 


Copper 

brush 

- 

- 

150 

to 

200 

Carbon 

- 

- 

30 

44 

50 

Copper 

sliding 

on  copper  - 

- 

60 

4 4 

100 

Brass 

“ brass 

- 

40 

4 4 

75 

Copper 

( ( 

“ phosphor-bronze 

50 

4 4 

80 

Copper 

screwed  on  copper 

- 

100 

4 4 

200 

4 4 

4 4 

“ brass  - 

- 

60 

4 4 

100 

44 

4 4 

“ phosphor-bronze 

60 

44 

100 

There  are  various  methods  of  supporting  the  resistance 
material  in  the  rheostat  which  in  all  commercial  types  must 
be  'absolutely  fire  -proof. 

A method  of  support  that  is  common  and  inexpensive, 
though  not  economical  of  space,  is  to  coil  the  wire  into  a 
helix.  Where  this  method  is  employed  the  helices  should 
have  a space  of  not  less  than 

d ==  .oiy/v  (20) 

inches  between  them  where  v is  the  voltage  at  the  termi- 
nals of  the  rheostat.  The  outside  diameter  of  the  helices 
should  vary  with  the  size  of  wire  used  and  may  be  de- 
termined approximately  from  the  equation, — 


100 


where  d,  is  expressed  in  inches. 


(21) 


The  helices  are  usually  mounted  in  a vertical  position,  so 
as  to  avoid  sagging  in  the  wire  when  heated,  but  the  hori- 
zontal position  allows  convection  currents  to  act  more 
effectively.  When  mounted  horizontally,  the  vertical  dis- 
tance between  helices  should  be  two  to  three  times  that 
indicated  by  equation  20.  The  length  of  helix  may  vary 
with  the  size  of  wire,  and  in  accordance  with  the  following 
expression : — * 

1 = ifm^  ‘ (22) 

where  1 is  the  length  of  the  helix  in  inches  and  m^.  seldom 
exceeds  30,000. 

The  number  of  turns  per  inch  in  length  of  helix  should 
be  such  that  when  stretched  in  position  there  is  about  one 
thirty-second  of  an  inch  space  between  consecutive  turns. 
The  several  helices  of  such  a resistance  may  have  each 
end  secured  by  passing  through  a porcelain  bushing  in  a 
metallic  end  plate,  which  must  be  carefully  proportioned 
as  the  combined  tension  of  many  helices  is  sometimes  very 
great.  A uniform  pressure  must  be  brought  upon  the 
porcelain  or  a fracture  may  result  in  a ground  on  the 
rheostat  frame. 

Another  convenient  method  of  mounting  is  to  place  all 
the  resistance  in  a continuous  helix  to  which  leads  may  be 
tapped,  and  which  is  wound  back  and  forth  over  large 
grooved  porcelain  insulators  strung  over  iron  rods  at  either 
end  of  the  rheostat  frame,  or  coiled  into  a flat  spiral  with 
asbestos  between  consecutive  turns. 


*E.  K.  Scott.  Metallic  Resistances,  The  Electrical  Review,  Vol  43,  p.  71 . 


H 


^ A method  that  is  often  used, 
a especially  for  rectangular  con- 
structor, consists  in  winding  the 
resistance  upon  a frame  shaped 
as  indicated  in  the  figure. 

With  this  construction  and  for 
small  wire  or  flat  conductor  the 
distance  pieces,  a,  a',  are  usually 
wound  with  asbestos  paper  and 


made  of  square  iron  rod  of  such  size  that  the  distance 
between  the  surfaces  of  conductors  is  from  tV  to  inch. 
The  following  equation  may  be  applied  for  the  calcula- 


tion  of  the  resistance  conductor  : 

l,=-^fe+1^2_4l,c+4c2 

^ b 

(23) 

s.-b  ] 

(24) 

(25) 

y=  S1I3 

(26) 

where,  c ==  distance  in  inches  between  centres  of  con- 
ductors in  adjacent  layers  (may  be  taken  at 

l//\ 

to  2 )• 

1^  = length  in  inches  of  a side  of  the  inside 
layer  (assumed  conveniently). 

= length  in  inches  of  a side  of  the  outside 
layer. 

I3  = length  of  a mean  turn  in  inches. 

b = number  of  turns  per  layer. 

Sj  ==  total  number  of  turns  in  frame. 


15 


Another  method  of  mounting  ribbon  conductor  in  a 
rheostat  is  to  wind  it  spirally  with  a narrow  strip  of  asbes- 
tos so  as  to  cover  about  one-half  its  surface  and,  when  so 
covered,  to  wind  the  conductor  into  a spiral  which  is  placed 
in  a frame  of  proper  shape  to  receive  it. 

Small  wire  of  high  resistance  can  be  wound  upon  mica 
cards  which  are  packed  in  a grooved  framework  holding 
the  cards  a small  distance  apart,  or,  after  being  wound, 
the  cards  may  be  stacked  with  alternating  strips  of  sheet 
mica  to  separate  them. 

A very  compact  rheostat  is  constructed  by  winding  the 
conductor  on  asbestos  tubes  about  one  inch  in  diameter 
and  a foot  long.  The  tubes  are  then  pressed  flat  and 
bent  into  a V shape  about  1.25  inches  wide  and  .25  inch 
depression.  They  are  stacked  with  iron  radiating  plates 
between  and  held  in  suitable  frames. 

There  are  several  special  types 
of  resistance  that  consist  of  a re- 
sistance conductor  embedded  in 
non-conducting  enamel  or  cement 
in  such  a manner  as  to  entirely 
confine  the  conductor  in  its  posi- 
tion, whatever  may  be  its  temper- 
ature, and  at  the  same  time  afford 
a large  radiating  surface.  The 
enamel  or  cement  is  usually  ap- 
plied to  cast-iron  plates  which  afford  mechanical  support 
and,  by  means  of  corrugated  or  ribbed  surfaces,  the  radi- 
ation of  heat  is  greatly  facilitated. 

The  enamels  used  consist  of  easily  fusible  salts,  such  as 
the  silicates  and  borates  of  sodium,  potassium  and  lead  to 
which  may  be  added  metallic  oxides  to  impart  the  desired 


i6 


color.  The  iron  radiating  plate  having  been  cleaned  with 
dilute  sulphuric  acid,  a powder  or  paste,  in  the  case  of 
Paris’s  composition  composed  of  130  parts  of  broken  flint 
glass,  20.5  parts  of  carbonate  of  soda  and  12  parts  of 
boracic  acid,  is  spread  over  it  and  the  whole  is  exposed 
in  a muffle  to  the  moderate  temperature  of  an  enamel 
furnace. 

Injurious  effects  of  contraction  and  expansion  of  the 
conductor  are  avoided  by  the  zigzag  form  into  which  it  is 
bent  so  that  there  is  little  danger  of  cracking  the  enamel 
from  this  cause.  The  result  of  this  construction  is  to 
greatly  reduce  the  necessary  length  and  cross  section  of 
resistance  conductor,  as  it  is  not  necessary  to  consider  its 
mechanical  strength  because  of  the  supporting  enamel, 
and  as  high  as  eight  or  ten,  or,  in  special  cases,  where  the 
heat  is  carried  away  by  running  water  in  contact  with  the 
radiating  plate,  25  watts  can  be  continuously  radiated  per 
square  inch  of  resistance  conductor  surface.*  At  the  tem- 
peratures usually  employed  for  this  class  of  resistance,  in 
the  neighborhood  of  200°C,  from  1.5  to  2.5  watts  per  square 
inch  of  outside  iron  surface  can  be  continuously  radiated, 
while,  for  short  intervals  of  not  more  than  15  seconds, 
from  6 to  10  watts  may  be  allowed  per  square  inch. 

In  designing  an  enamel  rheostat  or  resistance,  the  fol- 
lowing expressions  determine  close  approximations  to  the 
working  conditions  : f 


'T'  ^3  X Pq 

“ A„ 

(27) 

-r  83  X Pr 

A, 

(28) 

♦C.  E.  Carpenter,  Trans.  Am.  Inst.  Elect.  Eng’s,  Vol.  9,  p.  502. 
fW.  E.  Goldsborough,  Notes  on  Electrical  Design. 


17 


(29) 

(30) 


T„  = T,  + 


94  X P,  X d,  i.i8  X Pr  X d, 

■■  Ac  + Aj  Aj  + A, 


Po  + Pj.  is  the  total  amount  of  energy  liberated  in  the  re- 
sistance conductor  in  the  form  of  heat,  and  the  relative 
value  of  Pq  and  Pr  must  be  determined  from  the  last  two 
equations.  Therefore,  if; 


83  I 94  X d„  _ J. 

A„  ^ A„  + A, 


(31) 


(32) 

(33) 

(34) 


Where  : — 

Tg  = the  temperature  of  the  conductor  above  the 
air  in  degrees  centigrade. 

T„  = the  temperature  above  the  air  of  the  outside 
surface  of  the  enamel  in  degrees  centigrade. 

Tr  = the  temperature  above  the  air  of  the  outside 
surface  of  the  cast-iron  radiating  plate  in  degrees  centi- 
grade. 

Ac  = the  area  is  sq.  in.  of  the  surface  of  resistance 
conductor. 

Ao  = the  area  in  sq.  in.  of  the  outside,  or  exposed, 
surface  of  the  enamel. 

Ag  = the  area  in  sq.  in.  of  the  surface  of  contact 
between  the  enamel  and  the  radiating  plate. 

Aj.  = the  area  in  sq.  in.  of  the  outside,  or  exposed, 
surface  of  iron  radiating  plate. 


i8 


do  = the  average  distance  in  inches  between  the  sur- 
face of  the  conductor  and  the  outside  surface  of  the  enamel. 

dg  = the  average  distance  in  inches  between  the  sur- 
face of  the  wire  and  the  surface  of  contact  between  the 
radiating  plate  and  the  enamel. 

dr  — the  average  distance  in  inches  between  the 
outer  and  inner  surfaces  of  the  iron  radiating  plate. 

Pr  ==  the  watts  radiated  from  the  outside  surface  of 
the  radiating  plate. 

Pq  = the  watts  radiated  from  the  outside  surface  of 
the  enamel. 

To  determine  the  length  and  size  of  circular  sectioned 
resistance  conductor  to  be  embedded  in  the  enamel,  we 
have  : — 


(35) 


(36) 


K, 


where  L is  the  length  in  feet  and  is  taken  at  the  temper- 
ature determined  by  equation  (30). 

In  applying  the  above  expressions  to  the  calculation  of  a 
resistance,  the  following  method  is  perhaps  as  convenient  as 
any.  Allow  the  proper  rate  of  radiation  fromthe  surface  of  re- 
sistance conductor,  under  the  given  conditions,  which  deter- 
mines A^.  when  the  total  energy  to  be  liberated  is  known,  as 
is  usually  the  case.  Allow  the  proper  rate  of  radiation  from 
outside  surfaces,  which  are  usually  proportioned  so  that  the 
iron  surface  is  from  two  to  four  times  the  enamel  surface  and 
radiates  from  60  to  80  per  cent,  of  the  heat,  thus  determining 
A,,  and  A„.  and  may  now  be  determined  and  values 
of  d„,  d,.  and  d^  assumed  so  that  T,.  by  both  equations  has  the 
same  value.  Usually  A„  is  the  same  as  A^,  and  d^  the 


19 


same  as  d^,  or  two  or  three  times  greater,  depending  on 
conditions  of  construction,  but  always  as  small  as  possible 
on  account  of  the  low  radiating  coefficient  of  enamel.  Dj. 
maybe  from  .i  to  .3  inch,  depending  on  the  size  of  plate. 
It  is  sometimes  convenient  to  assume  d^  and  d^  and  solve 
for  dj.  in  the  second  equation  for  T^,  (30),  or  to  adjust  the 
values  of  and  as  indicated  by  the  structural  values 
necessary  for  d^,  dg  and  d^,  but  reasonable  temperatures 
must  always  be  employed ; and  the  value  of  T,,  must  be  used 
in  obtaining  the  resistance  of  the  conductor,  which,  on  ac- 
count of  the  high  temperatures  employed,  should  have  a 
small  temperature  coefficient. 

The  five  accompanying  diagrams  illustrate  several  of  the 


20 


1 


pdti 


ing  or  speed  controlling  rheostat  without  protective  devices. 
The  second  diagram  gives  connections  where  the  resistance 
is  automatically  inserted  under  a variety  of  conditions. 

A magnet  which  is  in  paral- 
lel with  the  motor  armature 
holds  the  contact  arm  in  po- 
sition against  the  action  of  a 
spring  so  long  as  there  is  any 
considerable  counter  electro- 
motive force  at  the  terminals 
of  the  armature.  Should 
the  current  be  removed  from 
the  mains  ; should  the  shun, 
circuit  of  the  motor  be 
broken  ; or  should  the  coun- 
ter E.  M.  F.  of  the  motor 
for  any  reason  become  low, 
the  spring  is  permitted  to 


r-AM/WWF 
\c 


act  and  resistance  is  in- 
serted independently  of 
what  may  be  the  cur- 
rent in  the  armature. 
A similar  form  of  rheo- 
stat having  the  release 
magnet  in  series  with 
the  armature  is  fre- 
quently used  but  does 
not  afford  as  perfect 
protection.  The  third 


Automatic  Motor 


21 


diagram  illustrates  a type  of  rheostat  which  will  protect  the 
motor  under  any  possible  conditions.  It  will  open  the 
circuit  if  there  is  a lower  E.  M.  F.  than  allowable;  if  the 
current  through  the  motor  becomes  excessive,  if  the  operator 
attempts  to  start  the  motor  too  quickly ; or  if  the  current 
be  taken  from  the  mains.  The  motor  cannot  have  the 
circuit  without  resistance  in  series  with  the  armature. 
The  fourth  diagram  is  of  a rheostat  frequently  used  where 
it  is  necessary  to  operate  a motor  automatically  or  to 
control  it  from  a distant  point.  Closing  the  switch 
operates  the  magnet,  by  the  magnetizing  coil,  c,  thus 
carrying  the  contact  arm  to  the  position  shown  as  the 
motor  increasesi  n speed.  A more  desirable  method  is 
to  connect  the  terminals  of  c at  e,  in  place  of  d,  as  shown, 
when  the  magnet  will  be  operated  simply  by  a current 
proportional  to  the  counter  E.  M.  F,  of  the  armature,  which 
protects  the  motor  under  all  conditions  except  overload,  and 
such  protection  may  be  otherwise  provided  for  by  circuit 
breaker  or  fuses.  The  rate  of  movement  of  the  contact  arm 
may  be  controlled  by  means  of  a dash  pot  with  valve  at  r or 
otherwise.  With  insufficient  current  in  c,  the  weight  of  the 

magnet  plunger  immediately 
raises  the  contact  arm  throw- 
ing in  all  resistance.  Similar 
results  are  secured  by  a device 
represented  in  the  fifth  diagram 
where  an  autouatic  rheostat  is 
secured  by  belting  a to  the 
motor  shaft  and  connecting  the 
magnet,  m,  across  the  armature 
or  line  as  conditions  may  re- 
quire. The  contact  arm,  b,  is  weighted  so  as  to  return  to 
position  cutting  in  all  resistance  whenever  m is  not  mag- 


22 


netized.  In  place  of  this  device,  a centrifugal  governor 
attached  to  the  motor  shaft  is  sometimes  emplo3'ed  for  mov- 
ing the  contact  arm,  and  in  many  cases  a small  motor 
on  an  independent  circuit  is  used  for  the  same  purpose. 

The  many  applications  of  electricity  to  the  heating 
of  street  railway  cars,  dwellings,  public  halls,  and  to 
laundry,  tinsmith,  welding,  forging,  annealing,  metallurgi- 
cal and  other  work,  make  the  principles  of  the  subject  im- 
portant to  the  electrical  engineer. 

The  relations  of  the  fundamental  quantities  involved  in 
this  work  are  expressed  by  Joule’s  law  : — 

E2t 

H = i2  Rt  = = Eit  (37) 

R 

i2  Rt  .24E2t 

or  =.24i2Rt= =.24  Eit  (38) 

4.2  R 

where  H is  the  heat  in  joules  and  is  the  heat  in  gramme- 
calories.  As  t is  the  time  in  seconds,  the  heat  per  hour  in 
gramme-calories  is 

864  E2 

H2  = 864  i2  R 864  Ei  (39) 

R 

which  is  a more  convenient  expression  for  most  engineering 
work,  and  is  applicable  to  any  portion  of  an  electric  circuit. 

The  temperature  produced  by  a current  in  a conductor  is 

.24  Eit 

T,  


w s 


(40) 


23 


where  is  the  rise  in  temperature,  in  degrees  centigrade, 
in  t seconds  and  w and  s are  the  weight  in  grammes  and 
the  specific  heat  of  the  conductor.  This  assumes  adiabatic 
action  which  is  only  approximately  secured  when  the  time 
is  very  short  and  the  conductor  is  well  protected  from  heat 
transferance.  Where  the  loss  of  heat  is  considerable,  as  is 
usually  the  case,  the  temperature  rises  until  the  rate  of  heat 
development  equals  the  rate  of  heat  transference  by  radia- 
tion or  otherwise,  which  may  be  expressed  as 


T,  K,  Kf  t = .24Eit 

(41) 

.24  Ei 

Ti  

(42) 

where  is  the  temperature  above  surroundings  when  con- 
stant conditions  have  been  reached,  is  the  heat  conduc- 
tivity of  the  envelope  of  the  conductor,  and  is  a constant 
depending  upon  the  dimensions  and  form  of  the  envelope. 
This  is  a more  general  form  of  equation  (i6)  in  which, 
when  applied  to  the  case  of  a bare  conductor,  should  be 
given  the  value  of  the  emissivity  of  the  substance  of  which 
the  conductor  is  built.  Equations  (3)  and  (27)  to  (30) are 
special  developments  for  the  cases  considered. 

Thermal  resistivities — reciprocals  of  conductivities — for 
the  different  substances  vary  considerably  with  slight  differ- 
ences in  composition  but,  in  the  absence  of  exact  determi- 
nations from  samples  of  the  material  to  be  used,  and  de- 
termined under  the  conditions  of  service,  the  following  table 
may  be  depended  upon  for  constants. 


24 


TABLE  VIII. 


MATERIAL 

, SPECIFIC  THERMAL. » 

KESISTIVITIBS.  CONDUCTIVITIES. 

Silver, 

•15 

to 

.20 

6.66 

to 

5.00 

Copper,  . . . 

.21 

(( 

•25 

4.76 

a 

4.00 

Zinc,  .... 

.80 

< ( 

.85 

1-25 

ti 

I. 18 

Brass, 

.80 

t ( 

.85 

1-25 

( ( 

I. 18 

Iron,  «... 

1. 10 

i i 

1.40 

.91 

( i 

•71 

Lead, 

1.80 

i ( 

2.00 

•55 

i i 

•50 

Ger.  Silver, 

2.25 

t i 

2.50 

•44 

i i 

.40 

Stone, 

40 

( ( 

70 

.025 

i i 

.014 

Glass, 

90 

t ( 

120 

.oil 

i ( 

.0083 

Sand,  . . . 

200 

i i 

300 

LO 

0 

q 

i i 

•0033 

Gutta-percha,  . 

400 

i i 

600 

.0025 

i i 

.0017 

Clay,  .... 

500 

( ( 

800 

.0020 

i i 

.0013 

Air,  . . . . 

1 100 

( ( 

1300 

.0009 

i i 

.0008 

Fine  Asbestos,  . 

1300 

1500 

.0008 

i i 

.0007 

Sawdust,  . . 

2000 

2500 

TO 

0 

0 

0 

( ( 

.0004 

Asbestos  Paper, 

2000 

( ( 

2900 

.0005 

i i 

.00035 

Wool,  . . . 

2000 

( ( 

3500 

.0005 

i i 

.00028 

Paper, 

2200 

( ( 

4000 

.00045 

4 4 

.00025 

Vulcanized  Rubber, 

2400 

( ( 

4500 

.00042 

4 4 

.00022 

Felt,  . . . . 

2600 

( ( 

5000 

.00038 

4 4 

.00020 

Slag  Wool,  . . 

3000 

( t 

5000 

.00033 

4 4 

.00020 

Loose  Wool, 

5000 

i i 

6600 

.00020 

4 4 

.00015 

The  values  appearing  in  the  table  are  expressed  in  C.  G. 
S.  units,  so  that  the  heat  transferance,  expressed  in  joules, 
is  readily  approximated  for  most  conditions  likely  to  arise. 
While  these  values  are  to  be  considered  as  only  approxi- 
mately correct,  yet  they  are  in  most  cases  within  limits 
of  variation  occasioned  by  differences  in  commercial  appli- 


'TV 


25 


cation.  Good  thermal  conductors  seem  to  conduct  better, 
and  good  thermal  insulators  to  insulate  better  with  decreas- 
ing temperatures. 


Oven.  One  Compartment. 


In  connection  with  the  above  the  following  abridgement 
of  a table,  prepared  by  H.  W.  Leonard,  is  convenient  in 
calculating  electric  heating  problems  and  designs  for  heat- 
ing apparatus. 


26 


TABLE  IX. 


Unit. 

Equivalent  Value  in  other  Units. 

1 

K.  W. 
Hour  = 

3,656,400  tt.  lbs. 

3,600,000  joules. 

3,440  heat  units. 

366,848  kilogram  metres. 

.229  lbs.  coal  oxidized 
with  perfect  efficiency. 
3 lbs.  water  evaporated  at 
313®  F. 

32.9  lbs. of  water  raised  from 
62°  to  212®  F. 

1 

H.  P. 
Hour  = 

1,980,000  ft.  lbs. 

3,580  heat  units. 

373,740  k.  g.  m. 

.173  lbs.  coal  oxidized 
with  perfect  efficiency. 
3.25  lbs.  water  evaporated 
at  213®  F. 

17.2  lbs.  water  raised  from 
63®  F,  to  212®  F. 

1 

K W.  = 

3,656,400  ft.  lbs.  per  hour. 

4,424  ft.  lbs.  per  minute. 

73.73  ft.  lbs.  per  second. 
3,440  heat  units  per  hour. 

573  heat  units  per  minute. 

9.55  heat  units  per  second. 
.23g  lbs.  coal  oxidized  per 
hour. 

3 lbs.  water  evaporated  per 
hour  at  212®  F. 

1 

H.  P.  = 

2,580  heat  units  per  hour. 

43  heat  units  per  minute. 

.71  heat  units  per  second, 

.172  lbs.  coal  oxidized  per 
hour. 

2.25  lbs.  water  evaporated  per 
hour  at  312®  P'. 

1 

Joule 

.00000278  K.  W.  hour. 

.102  k.  g.  m. 

.00094  heat  units. 

•73  lbs. 

Unit. 

Equivalent  Value  in  other  Units. 

1 

Ft.  Lb.  = 

1.36  joules. 

.1383  k.  g.  m. 

.000000377  K.  W.  hours. 
.000291  heat  units. 

.0000005  H.  P.  hour. 

1 

Watt  = 

.00134  H.  P. . 

3.44  heat  units  per  hour. 

.73  ft.  lbs.  per  second. 

.003  lbs.  of  water  evaporated 
per  hour. 

44.24  ft.  lbs.  per  minute. 

1 

Heat 
Unit  = 

1,048  Watt  seconds. 

773  ft.  lbs. 

352  calories,  (g.  d.) 

108  kilogram  metres. 

.000291  K.  W.  hour. 

.000388  H.  P.  hour. 

.0000667  lbs.  coal  oxidized. 
.00087  lbs.  water  evaporated 
at  312®  F. 

1 Lb.  Bitu- 
minous 
Coal  Oxi- 
dized with 
perfect  ef- 
ficiency = 

15.000  heat  units. 

.98  lbs.  Anthracite  coal  oxi- 
dized. 

3.1  lbs.  dry  wood  oxidized. 

15  cu.  ft.  illuminating  gas. 

4.37  K.  W.  hours  (theoretical 
value.) 

5.81  H.  P.  hours  (theoretical 
value.) 

11.590.000  ft.  lbs.  (theoretical  value.) 
13.1  lbs.  of  water  evaporated  at 

ZI3®  F. 

ILb. 

Water 

Evapora- 

ted 

212"  F.= 

.33  K.  W.  hour. 

.44  H . P.  hour. 

1,148  heat  units. 

124,300  k.  g.  m. 

1,319,000  joules. 

887,800  ft.  lbs. 

.076  lbs.  of  ooal  oxidized. 

27 


The  heating  of  street  railway  cars,  because  of  the  con- 
venience, saving  of  space,  cleanliness,  and  ease  of  control 
offered  by  the  method,  is  the  most  important  commercial 
application  of  electric  heating,  though  the  cost  of  heat  de- 
livered to  the  car  is  frequently  greater  than  if  furnished  by 
a small  stove.  In  most  instances  however,  the  advantages 
offered  by  electric  heaters  so  far  over  balance  any  adverse 
difference  in  cost  that  they  are  almost  universally  employed 
on  electrically  operated  lines. 

The  conditions  under  which  cars  are  to  be  heated  vary 
with  climatic  differences  and  character  of  line  on  which 
they  are  to  be  used,  so  that  it  is  sometimes  difficult  to  make 
an  accurate  estimate  of  the  energy  required,  but  there  is 
data  available  which  will  enable  such  estimates  to  be  made 
in  most  instances  and  the  following  will  be  found  of  value  : 


TABLE  X.* 


^CARS.-^ 

DOORS.  WINDOWS. 

CU.  FT. 

r-TEMP.  FAHR.-x 

OUTSIDE.  INSIDE. 

WIND. 

MILES. 

WATTS. 

2 

12 

850-5 

28° 

51-59° 

25 

2295 

2 

12 

850-5 

7° 

34°-44°  ' 

28 

2325 

2 

12 

808.5 

28° 

47°-52° 

25 

2180 

2 

12 

913-5 

35° 

40°-64'’ 

3 

2745 

4 

16 

1012. 4 

7° 

4i°-5o° 

28 

3038 

4 

16 

1012. 4 

28° 

48°-6o‘’ 

25 

3160 

McElroy  gives  .08  B.  T.  U.  per  second  as  the  amount  of 
heat  necessary  for  a car  under  average  conditions  per  de- 
gree Fahrenheit  difference  in  temperature  between  inside 
and  outside  of  car.f  The  fact  that  an  average  person 
radiates  heat  at  about  .053  B.  T.  U.  per  second  has  an  im- 
portant bearing,  depending  upon  the  crowding  of  the  cars. 


* Atlantic  Avenue  (Boston)  Railway  Tests, 
t J.  F.  McElroy,  Electrical  World,  Vol.  26,  p.  374. 


28 


as  40  to  50  people  will  supply  sufRcient  heat  for  the  car, 
2.5  B.  T.  U.  per  second,  under  average  conditions,  though 
6 to  10  B.  T.  U.  per  second  may  be  necessary  in  the  most 
severe  weather. 

Iron  wire,  not  only  because  of  its  low  cost,  but  also  be- 
cause of  its  high  temperature  coefficient,  is  particularly 
valuable  in  the  construction  of  heaters,  as  its  resistance  will 
increase  so  as  to  keep  the  current  at  a safe  value,  if  for  any 
reason  the  free  radiation  of  heat  be  interrupted  so  that  the 
temperature  of  the  heater  rises. 


It  is  important  to  use  two  or  more  heaters  in  a car  so 
that,  by  a properly  arranged  switch,  they  may  be  placed  in 
series,  series-parallel,  or  in  parallel  across  the  line,  and 
thus  secure  a convenient  means  of  regulating  the  liberation 
of  heat. 


Menting  Coll 


The  following  are  some  methods  of  mounting  car  heat- 
ers. In  one  heater  the  German  silver  wire,  bent  in  a zig- 
zag form,  is  embedded  in  powdered  fire  clay  between  two 


29 


rough  iron  castings.  In  another  heater  No.  20  B.  & S. 
galvanized  iron  wire  is  wound  in  a spiral  groove  on  cylind- 
rical porcelain  tubes  slipped  over  a ^ inch  square  iron  rod. 
Many  other  forms  are  employed  but,  in  general,  they  may 
be  said  to  consist  essentially  of  a galvanized  iron,  or  Ger- 
man silver,  wire  coiled  or  wound  so  as  to  present  as  large 


Portable  Heater. 


, a radiating  surface  as  possible  in  air,  or,  to  increase  radia- 
tion and  convection,  and,  at  the  same  time,  secure  the  nec- 
essary resistance  within  a small  space,  the  wire  is  often 
wound  in  a helix,  which  in  turn  is  wound  on  a porcelain  or 
other  non-combustible  block,  tube,  rod  or  pins.  The  heater 
must  be  thoroughly  insulated,  absolutely  fire  proof,  and, 
unless  the  conductor  is  embedded  in  enamel,  its  temperature 
must  be  kept  below  that  at  which  either  oxidization  or  crys- 
tallization is  liable  to  occur.  While  the  conversion  of 
electrical  energy  into  heat  is  perfect,  so  far  as  the  heater  is 
concerned,  and  the  efficiency  of  an  electric  heater  regarded 
in  this  way  is  the  highest  attainable,  yet,  to  secure  the  best 
diffusion  of  heat  through  a given  space,  the  heater  should 
not  be  operated  at  too  high  a temperature  and  should  be  so 
designed  as  to  permit  the  free  passage  of  air  currents  over 
its  surfaces. 


30 


The  cost  of  operating  car  or  other  electric  heaters  varies 
with  the  cost  of  current  supply  which,  in  turn,  depends 
upon  the  price  of  coal  and  local  conditions  of  plant  opera- 
tion, so  that  from  1.5  to  8 cents  per  Kw.  hour  may  be  ex- 
pected as  the  conditions  are  more  or  less  favorable.*  Under 
usual  conditions  of  power  development  it  may  cost  from  25 
to  50  cents  per  car  day  of  20  hours,  depending  upon  the 
weather  and  size  of  the  railway  system.  Knowing  local 


conditions  of  operation  in  any  instance,  the  foregoing  gives 
a basis  of  reasonably  exact  determination  of  design  and 
costs. 

Where  alternate  currents  are  employed  for  electric  heat- 
ing, it  is  usually  advisable  to  design  the  heater  so  that 
the  development  of  hysteresis  and  eddy  current  losses  in 
iron  coils  facilitates  the  conversion  to  heat  energy,  except 
where  the  heater  may  be  used  on  either  a D.  C.  or  an  A. 
C.  circuit  of  any  wave  form  or  frequency. 

For  the  heating  of  buildings,  welding  and  miscellaneous 
electric  heating  apparatus,  the  following  data  is  of  value  in 
designing  this  class  of  appliances  and  in  the  estimation  of 
costs  of  operation. 


Chas.  E.  Emerj,  Cost  of  Steam  Power.  Trans.  Am.  Inst.,  Elect.  Eng’s. 
Vol.  10,  p.  119. 


31 


Electric  Welding.  (Thomson  System.) 
TABLE  XL* 


IRON  AND  STEEL. 

BRASS. 

COPPER. 

Area  in 
Sq.  In. 

Watts  in 
Prim’y  of 
Welders. 

Time  in 
Seconds. 

Area  in 
Sq.  In. 

Watts  in 
Prim’y  of 
Welders. 

Time  in 

Seconds. 

Area  in 
Sq.  In. 

Watts  in 
Prim’y  of 
Welders. 

Time  in 

1 Seconds.] 

0-5 

8550 

33 

•25 

7500 

17 

.125 

6000 

8 

I.O 

16700 

45 

•50 

13500 

22 

.250 

14000 

II 

1-5 

23500 

55 

•75 

19000 

29 

•375 

19000 

13 

2.0 

29000 

65 

1. 00 

25000 

33 

.500 

25000 

16 

2.5 

34000 

70 

1-25 

31000 

38 

.625 

31000 

18 

3-0 

39000 

78 

1.50 

36000 

42 

•750 

36500 

21 

3-5 

44000 

85 

1-75 

40000 

45 

•875 

43000 

22 

4.0 

50000 

90 

2.00 

44000 

48 

1. 000 

49000 

23 

TABLE  XII. t 


WELD. 

2 in.  Iron  Bar  > 

Average  of  2 Welds,  5 

TIME  IN  SEC.  WATTS. 

249  42522 

in.  R’d.  Iron  Bar,  > 
Average  of  15  Welds,  > 

57 

13204 

I in.  Bessemer  Steel  Shaft,  } 
Average  of  4 Welds,  ] 

> 61 

17680 

^ in.  Bessemer  Steel  Shaft,  } 
Average  of  4 Welds,  ] 

; 45 

1 1860 

in.  Bessemer  Steel  Shaft,  } 
Average  of  4 Welds,  ] 

> 26 

6789 

* Hermann  Lemp,  Electric  Welding  and  Metal  Working.  Engineering 
Mag.,  Vol.  7,  p.  691. 

tB.  A.  Dobson,  Electric  Welding.  Elect.  Rer.  (London;  Vol.  35,  p.  133. 


32 


COOKING. 

An  oven  roasting  meat  takes  2750  watts  and  7 to  8 
minutes  per  pound  of  meat  roasted. f Frying  pan,  275 
watts.  Coffee  pot,  500  watts.  Four  quart  tea  kettle, 
700  watts,  boils  one  quart  in  10  minutes.  One  quart 
chafing  dish,  500  watts.  Two  quart  stew  pan,  700  watts. 
A ten  course  dinner  has  been  prepared  for  120  people  with 
60  Kw.  hours  electrical  energy,  which  at  8 cents  per  Kw. 
hour  gives  cost  per  person  as  4 cents.*  Broiler  for  two 
steaks,  15  to  20  minutes,  1200  to  1500  watts.  Farina 
boiler  100  to  450  watts  for  one  quart  or  200  to  700  watts 
for  two  quarts.  Small  oven,  2100  cubic  inches,  350  to 
1500  watts.  Hot  water  urn,  five  gallons,  from  450  to  1750 
watts. 

MISCELLANEOUS. 

Soldering  irons,  200  to  350  watts.  Laundry  irons,  200 
to  400  watts.  One  gallon  glue  pot,  250  to  1100  watts. 
One  quart  glue  pot,  700  watts.  One  pint  glue  pot,  500 
watts.  To  keep  glue  melted,  50  to  100  watts.  Curling 
tongs  heater,  50  watts.  Sealing  wax  heater,  50  watts. 
Troy  polishing  iron,  330  watts.  Nine  pound  heavy 
laundry  iron,  650  watts.  Twelve  pound  goose,  650  watts. 
Twenty-five  pound  goose,  800  watts.  Heating  pad,  400 
to  1100  watts.  Solder  pot,  four  pounds,  100  to  200  watts; 
ten  pounds,  200  to  400  watts.  One  joule  per  second,  or 
one  watt,  will  raise  one  cubic  foot  of  air  .055°  F.  per  second, 
or  18  watts  will  raise  one  cubic  foot  of  air  1°  F.  per  second. 


t A.  V.  Abbott,  Electrical  Trans.  ofEnergj’^,  p.  298. 
* Ifouston  and  Kennelley,  Electric  Heating,  p.  i78. 


